Determine the nth term of the sequence $\frac { 1 } { 2 ^ { 2 } } , \frac { 2 } { 3 ^ { 2 } } , \frac { 3 } { 4 ^ { 2 } } , \frac { 4 } { 5 ^ { 2 } } , \ldots$ . Assume that n starts at 1.

A) $\frac { n } { ( n + 1 ) ^ { 2 } }$
B) $\frac { n - 1 } { ( n + 1 ) ^ { 2 } }$
C) $\frac { n } { 2 ^ { n } }$
D) $\frac { n + 1 } { n ^ { 2 } }$
E) $\left( \frac { n } { n + 1 } \right) ^ { 2 }$

Question

Determine the nth term of the sequence $\frac { 1 } { 2 ^ { 2 } } , \frac { 2 } { 3 ^ { 2 } } , \frac { 3 } { 4 ^ { 2 } } , \frac { 4 } { 5 ^ { 2 } } , \ldots$ . Assume that n starts at 1.

A) $\frac { n } { ( n + 1 ) ^ { 2 } }$
B) $\frac { n - 1 } { ( n + 1 ) ^ { 2 } }$
C) $\frac { n } { 2 ^ { n } }$
D) $\frac { n + 1 } { n ^ { 2 } }$
E) $\left( \frac { n } { n + 1 } \right) ^ { 2 }$

Quizplus · Accepted Answer

The nth term of the given sequence is $\frac{n}{(n+1)^2}$, as each term is formed by dividing the position number $n$ by the square of the next number $(n+1)^2$.

Determine the Nth Term of the Sequence 122,232,342,452,…\frac { 1 } { 2 ^ { 2 } } , \frac { 2 } { 3 ^ { 2 } } , \frac { 3 } { 4 ^ { 2 } } , \frac { 4 } { 5 ^ { 2 } } , \ldots221​,322​,423​,524​,…

Determine the Nth Term of the Sequence $\frac { 1 } { 2 ^ { 2 } } , \frac { 2 } { 3 ^ { 2 } } , \frac { 3 } { 4 ^ { 2 } } , \frac { 4 } { 5 ^ { 2 } } , \ldots$